Algebra Examples

$\log (x) + \log (3) = 2 \log (4) - \log (2)$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (x \cdot 3) = 2 \log (4) - \log (2)$

Step 1.2

Move $3$ to the left of $x$ .

$\log (3 x) = 2 \log (4) - \log (2)$

Step 2

Simplify the right side.

Tap for more steps...

Step 2.1

Simplify $2 \log (4) - \log (2)$ .

Tap for more steps...

Step 2.1.1

Simplify each term.

Tap for more steps...

Step 2.1.1.1

Simplify $2 \log (4)$ by moving $2$ inside the logarithm.

$\log (3 x) = \log (4^{2}) - \log (2)$

Step 2.1.1.2

Raise $4$ to the power of $2$ .

$\log (3 x) = \log (16) - \log (2)$

Step 2.1.2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log (3 x) = \log (\frac{16}{2})$

Step 2.1.3

Divide $16$ by $2$ .

$\log (3 x) = \log (8)$

Step 3

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$3 x = 8$

Step 4

Divide each term in $3 x = 8$ by $3$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $3 x = 8$ by $3$ .

$\frac{3 x}{3} = \frac{8}{3}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{8}{3}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{8}{3}$

Decimal Form:

$x = 2.\overline{6}$

Mixed Number Form:

$x = 2 \frac{2}{3}$